Fuzzy-Model-Based Sliding Mode Control of Nonlinear Descriptor Systems.

Area of Science:

• Control Systems Engineering
• Fuzzy Logic Systems
• Nonlinear Dynamics

Background:

• Uncertain time-delay nonlinear descriptor systems pose significant control challenges.
• Existing sliding mode control (SMC) methods have limitations in handling diverse subsystem input matrices and time delays.

Purpose of the Study:

• To develop a novel integral fuzzy switching manifold for uncertain time-delay nonlinear descriptor systems.
• To design robust fuzzy SMC controllers that accommodate input saturation and unknown uncertainties.

Main Methods:

• Utilizing Frobenius' theorem and double orthogonal complement to establish the existence of the fuzzy manifold.
• Analyzing reachability conditions for synthesizing the fuzzy SMC controller.
• Developing an adaptive fuzzy SMC controller for enhanced robustness.

Main Results:

• A new integral fuzzy switching manifold is proposed, allowing for diverse input matrices across subsystems.
• Admissibility conditions for sliding motion with strict dissipation are derived.
• A feasible fuzzy SMC controller and an adaptive version are synthesized and validated.

Conclusions:

• The proposed integral fuzzy switching manifold significantly improves the applicability of SMC for complex systems.
• The developed controllers effectively manage uncertainties and input saturation, ensuring system stability.
• The method's effectiveness is confirmed through practical implementation on a pendulum system.